Membranes (or separators) are critical for ionic conduction and electronic isolation in many electrochemical devices. For cell architectures that utilize redox-active species that are dissolved, dispersed, or suspended in electrolyte, including fuel cells (FCs), redox flow batteries (RFBs), and conversion reaction electrodes, it is also of value that the membrane prevent active material crossover that would otherwise contribute to device shorting, electrode fouling, or irrevocable loss in capacity. Unfortunately, commercial battery separators, which feature shape-persistent mesopores, are freely permeable to most active materials used in RFBs and electrolyte soluble intermediates formed in conversion reaction electrodes. Alternative membrane separators have thus far relied heavily on variants of aqueous single-ion conductors, e.g., Nafion, which may ultimately restrict the use of certain types of flowable electrodes. Despite the wide availability of porous materials that might serve effectively as membrane components, including zeolites, metal-organic frameworks, covalent organic frameworks, carbon nanotubes, cyclic peptide nanotubes, and microporous polymers, rational design rules for achieving ion-selective transport via sieving in battery membranes have not been established.